Gridless DOA Estimation with Multiple Frequencies

TL;DR

This paper introduces a gridless DOA estimation method using atomic norm minimization for multi-frequency signals, providing a convex optimization approach with theoretical guarantees and robustness against aliasing.

Contribution

It formulates multi-frequency DOA estimation as an atomic norm minimization problem and offers a dual certificate condition for optimality, addressing spatial aliasing issues.

Findings

The proposed method accurately localizes sources using SDP.

Dual polynomial construction certifies the solution's optimality.

Numerical results demonstrate robustness against aliasing.

Abstract

Direction-of-arrival (DOA) estimation is widely applied in acoustic source localization. A multi-frequency model is suitable for characterizing the broadband structure in acoustic signals. In this paper, the continuous (gridless) DOA estimation problem with multiple frequencies is considered. This problem is formulated as an atomic norm minimization (ANM) problem. The ANM problem is equivalent to a semi-definite program (SDP) which can be solved by an off-the-shelf SDP solver. The dual certificate condition is provided to certify the optimality of the SDP solution so that the sources can be localized by finding the roots of a polynomial. We also construct the dual polynomial to satisfy the dual certificate condition and show that such a construction exists when the source amplitude has a uniform magnitude. In multi-frequency ANM, spatial aliasing of DOAs at higher frequencies can cause challenges. We discuss this issue extensively and propose a robust solution to combat aliasing. Numerical results support our theoretical findings and demonstrate the effectiveness of the proposed method.